Feel free to experiment with adding fresh herbs if you have them around. I’ve made this with a heaping tablespoon of fresh dill and it was wonderful. A handful of fresh cilantro is nice, too. I generally end up adding about 1/4 cup of water to thin the sauce to where I like it, so feel free to use more or less depending on how thick you’d like yours. You can also always thin it out as you use it each time.
Preheat the oven to 350 F and toast the walnuts until fragrant, about 7-9 minutes. Set aside to cool completely.
Increase the temperature to 400 F and roast the scallions with 1 tablespoon olive oil (or enough to lightly coat each) until wilted and slightly charred on the tops, about 12-14 minutes. Allow to cool and slice off and discard the white, nubby bottoms.
Place cooled walnuts in the food processor and grind until fine. Add the scallions, parsley, salt, lemon juice, vinegar and 1/4 cup olive oil. Process until smooth. The sauce should be the consistency of a thick pesto. If it’s too thick, add water, 1 tablespoon at a time, to get a spoon-able consistency that you’re happy with.
Refrigerate in an airtight container for 2-3 weeks.